Nonlinear modeling and vibration analysis of a two-link flexible manipulator coupled with harmonically driven flexible joints

Abstract The present paper deals with the theoretical studies to determine the modal parameters and investigate the dynamic instability of a harmonically driven planar two-link manipulator with flexible joints. An appropriate dynamic model incorporating both link and joint flexibilities subjected to a harmonic motion has been developed while joint flexibility has been modeled as a combination of torsional spring-inertia elements. Modal parameters for various modes of vibration have been evaluated and graphically demonstrated. Then, method of multiple scales has been employed to further analyze the vibration attributes of steady state responses and their stability under resonance condition. The comparative mode shapes and bifurcation diagrams those describe the vibrating system have been illustrated to demonstrate the dynamics of the flexible manipulator. The effect of geometric and inertial coupling existing between the flexible arms on bifurcation states and stability of the obtained solutions has been thoroughly investigated. Analytically obtained results have been verified numerically and found to be in good agreement. The present theoretical results deliver a useful insight into the attributes of vibration characteristics along with the nonlinear dynamic behavior and operational stability of two-link flexible manipulator under joint motion.

[1]  Moharam Habibnejad Korayem,et al.  Accurate nonlinear modeling for flexible manipulators using mixed finite element formulation in order to obtain maximum allowable load , 2015 .

[2]  Safya Belghith,et al.  Self-generated limit cycle tracking of the underactuated inertia wheel inverted pendulum under IDA-PBC , 2017 .

[3]  Morteza Moradi,et al.  Neural Network Identification Based Multivariable Feedback Linearization Robust Control for a Two-Link Manipulator , 2013, Journal of Intelligent & Robotic Systems.

[4]  Helmut Schwarz,et al.  Adaptive augmented state feedback control for an experimental planar two-link flexible manipulator , 1998, IEEE Trans. Robotics Autom..

[5]  X Zhang,et al.  Comparison of some modeling and control issues for a flexible two link manipulator. , 2004, ISA transactions.

[6]  Wu Jun,et al.  Workspace and dynamic performance evaluation of the parallel manipulators in a spray-painting equipment , 2017 .

[7]  Safya Belghith,et al.  Diversity in the nonlinear dynamic behavior of a one-degree-of-freedom impact mechanical oscillator under OGY-based state-feedback control law: Order, chaos and exhibition of the border-collision bifurcation , 2018, Mechanism and Machine Theory.

[8]  Eko Supriyanto,et al.  Principal vibration modes of a rigid-flexible manipulator , 2017, 2017 International Conference on Robotics, Automation and Sciences (ICORAS).

[9]  M.A. Ahmad,et al.  Dynamic modelling of a two-link flexible manipulator system incorporating payload , 2008, 2008 3rd IEEE Conference on Industrial Electronics and Applications.

[10]  Jimoh O. Pedro,et al.  Hybrid NNMPC/PID control of a two-link flexible manipulator with actuator dynamics , 2015, 2015 10th Asian Control Conference (ASCC).

[11]  Ji Wang,et al.  Adaptive simultaneous motion and vibration control for a multi flexible-link mechanism with uncertain general harmonic disturbance , 2017 .

[12]  Atef A. Ata,et al.  Dynamic analysis of a two-link flexible manipulator subject to different sets of conditions , 2012 .

[13]  Shaoping Wang,et al.  Robust adaptive motion/force control for motion synchronization of multiple uncertain two-link manipulators , 2013 .

[14]  Badri Narayan Subudhi,et al.  Robust tip trajectory synchronisation between assumed modes modelled two-link flexible manipulators using second-order PID terminal SMC , 2017, Robotics Auton. Syst..

[15]  Asaji Sato,et al.  Experimental analysis of the two-link manipulator in consideration of the relative motion between link and object , 2015, Artificial Life and Robotics.

[16]  Akira Abe,et al.  A novel feedforward control technique for a flexible dual manipulator , 2015 .

[17]  H Karagülle,et al.  Vibration control of a two-link flexible manipulator , 2017 .

[18]  Shang–Teh Wu,et al.  Vibration attenuation of a two-link flexible arm carried by a translational stage , 2018 .

[19]  Jun Wu,et al.  Mechatronics modeling and vibration analysis of a 2-DOF parallel manipulator in a 5-DOF hybrid machine tool , 2018 .

[20]  Asaji Sato,et al.  Analysis of the two-link manipulator in consideration of the horizontal motion about object , 2015, Artificial Life and Robotics.

[21]  Leonard Meirovitch,et al.  Methods of analytical dynamics , 1970 .

[22]  Seung-Bok Choi,et al.  Compliant control of a two-link flexible manipulator featuring piezoelectric actuators , 2001 .

[23]  Linjun Zhang,et al.  Adaptive boundary control for flexible two-link manipulator based on partial differential equation dynamic model , 2013 .

[24]  Xiaoping Zhang,et al.  PDE modeling and control of a flexible two-link manipulator , 2005, IEEE Transactions on Control Systems Technology.

[25]  Kyoungchul Kong,et al.  Two-Degree-of-Freedom Control of a Two-Link Manipulator in the Rotating Coordinate System , 2015, IEEE Transactions on Industrial Electronics.

[26]  Wei Ding,et al.  Analysis of transient deformation response for flexible robotic manipulator using assumed mode method , 2017, 2017 2nd Asia-Pacific Conference on Intelligent Robot Systems (ACIRS).

[27]  Jun Wu,et al.  Dynamics and control of a planar 3-DOF parallel manipulator with actuation redundancy , 2009 .

[28]  Akira Abe,et al.  Trajectory planning for residual vibration suppression of a two-link rigid-flexible manipulator considering large deformation , 2009 .

[29]  Yang Yu,et al.  Back-stepping control of two-link flexible manipulator based on an extended state observer , 2015 .